Reduction of Chern-Simons-Schrödinger Systems in One Space Dimension
Reduction of Chern-Simons-Schrödinger Systems in One Space Dimension
We study Chern-Simons-Schrödinger systems in one space dimension. We show that Chern-Simons-Schrödinger and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>𝒩</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:math>supersymmetric Chern-Simons-Schrödinger equations can be reduced, under the gauge condition<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>≡</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:math>, to equations of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow></mml:math>only which are coupled cubic Schrödinger systems.